The logical bases of education

Front matter

.HO,

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Edited by

Chapter I Page

5 1. Education and Knowledge 1

5 2. Knowledge and Truth 1

3 3. Knowledge and Superstition 2

I 4. Knowledge and Belief 4

) 5. Savage Philosophy 7

I 6. Explanation of the World as a Sum of Things. . 9

I 7. Explanation of the World by Laws 11

Factors of Change . 12

Necessity and Universality of Law .... 14

Atoms and Energy 15

I 8. Explanation of the World as System 16

\ 9. Nature of Reality and of Knowledge 1&

The Test of Truth 23

110. The World as Mental Construction 24

Chapter II

1. The Factors of Knowledge 27

3. The Postulates at the Stage of Sense-perception . 29

Identity 29

Contradiction 29

Excluded Middle 30

Sufficient Reason 31

Contents

PAGE

4. The Postulates at the Stage of Law 31

Causation 33

Chapter III Knowledge And Language

1. Ideas and I^owledge 42

i 2. Ideas and Reality 42.

1 3. Ideas and Images 43 ;

Thought and Imagination 43

I 4. Development of Ideas 45

i 5. Ideas and Language 45

(6. Language and Communication of Knowledge . . 46

! 7. Verbal Language 46

Writing 47

! 8. Language and Learning 48

( 9. Spoken and Written Language 49

510. Meaning and Context 50

Specific and General Meanings of Words . ■ . 53

511. Ambiguities of Language 55

Ambiguities in Individual Words 55

Ambiguities in Construction 60

Chapter IV Knowledge And Logic

^ 1. Nature of Logic 62

5 2, Nature of Judgment 6Si

^ 3. Judgments and Logic -60

CONTENTS xi

PAGE

§ 4. Abstract Nature of Thought 64

§ 5. Form and Matter 65

§ 6. Logic is Abstract and Formal . 66

§ 7. Function of Logic 67

§ 8. Value of Logic 68

Chapter V Nature Of Judgment

§ 1. Judgment and Proposition 69

§ 2. Judgment and Truth 70

§ 3. Judgment and Experience 72

§ 4. Judgment is an Act of both Analysis and

Synthesis . 73

§ 5. Subject and Predicate 75

§ 6. Copula 77

§ 7. Relative Prominence of Analysis and Synthesis

in Judgments 78

§ 8. Summary 78

Chapter VI Types Of Judgment

Main Types of Judgment 80

Development of Judgment 81

Impersonal Judgments 81

Demonstrative Judgments 82

Judgments of Particular Relation .... 82

Historical Singular Judgments 83

Enumef ative Judgments 83

Search for the Universal Judgment .... 84

The Generic Judgment 85

The Hypothetical Judgment 85

Reciprocal Universal Judgments ..... 88

The Disjunctive Judgment 88

Negation 91 ii CONTENTS

PAGE

4. Quality and Quantity in Categorical Judgments . 94

5. Quality and Quantity in Hypothetical and Dis-

junctive Judgments 96

Chapter VII Formal Relations Of Propositions

1. The Four-fold Scheme of Propositions 97

2. Distribution of Terms 98

3. Conversion 99

4. Modes of Opposition 101

Subalternation 101

Contradiction 102

Contrariety 102

Sub-contrariety 103

Summary of Opposition 103

Chapter VIII The Method Of Knowledge

1. Truth and Evidence 104

2. Nature of Method 104

3. Development of Doctrine of Method 105

Aristotle , 105

Mediaeval Logic 105

Bacon 106

Newton 107

Mill 107

Modern Logic 108

4. Method and Thought 108

5. Method and Facts 109

6. Inferential Character of Method . . ' 110

7. Characteristics of Methodical Thought Ill

Purpose Ill

Definite Starting-point 112

8. Fallacies incidental to Method 112

Petitio Prindpii 112

Ignoratio Elenchi 114

CONTENTS xiii

PAGE

§ 9. Essence of Methodical Process 116

§10. Nature of Inference 116

Inference and System 117

Inference and Previous Knowledge .... 118

Inference and Universals 119

§11. Deductive and Inductive Inference 119

§12. Analysis and Synthesis 121

§13. Analytic and Synthetic Methods 122

Chapter IX Deductive Inference

§ 1. Kinds of Deductive Inference 123

SYLLOGISM

§ 2. Nature of Syllogism 124

Distributed Middle Term 124

Conclusion warranted by Premises .... 127

Validity of Syllogism 128

Minor Rules of Syllogism ........ 129

§ 3. Forms of Syllogism 129

§ 4. Hypothetical Syllogisms 130

CONSTRUCTION

§ 5. Nature of Construction " 132

§ 6. Types of Construction 133

Arithmetical Constructions 133

Geometrical Constructions 135

§ 7. Inductive Aspect of Construction 135

Chapter X Outline Of Inductive Method

§ 1. Meaning of ' Induction ' 136

§ 2. General Method of Induction 137

§ 3. Direct and Indirect Testing of Hypotheses ... 138 xiv COKTENTS

Chapter XI Observation

PAGE

§ 1. Importance of Observation 140

§ 2. Liability of Observation to Error 140

§ 3. Dependence of Observation on Previous Knowledge 141

§ 4. Observation and Inference 142

Selection 142

Recognition 143

Distinction between ' Observation ' and

' Inference ' 147

§ 5. Observation and Prejudice 149

§ 6. Observation and Scientific Instruments 150

§ 7. Experiment 150

Chapter XII Testimony

§ 1. Necessity of Testimony 153

§ 2. Reception of Testimony 154

§ 3. Tests of Testimony 155

Good Faith 156

Accuracy 158

§ 4. Anonymous Testimony 160

§ 5. Corroboration of Testimony 162

Tradition 163

Independent Corroboration 164

§ 6. Inference from Absence of Testimony 164

Chapter XIII Hypotheses

§ 1. Nature of Hypotheses 166

§ 2. Origin of Hypotheses 167

§ 3. Hypotheses and Facts 168

Danger of Bias 170

CONTENTS XV

PAGE

§ 4. Testing of Hypotheses 171

§ 5. Descriptive and Working Hypotheses 172

§ 6. Permissible Hypotheses 173

8 7. Crucial Instances 174

Chapter XIV Direct Development Of Hypotheses

1. Accidental Coincidences and Necessary Connexions 177

2. Empirical Generalization and Enumerative In-

duction 178

3. Analogy 180

4. Nature of Direct Methods in Induction 184

5. Method of Agreement . 188

6. Method of Exclusions 191

7. Method of Difference 192

8. Method of Concomitant Variations 195

9. Method of Residues 200

10. Example of Use of Methods : Colour of Animals . 200

Chapter XV Indirect Verification Of Hypotheses

1. Relation of Indirect to Direct Methods 204

2. Initial Use of Indirect Method 205

Circumstantial Evidence 206

3. The Indirect Method in History . 207

4. The Indirect Method in Geology and Biology . . 208

5. Establishment of the Theory of Gravitation . . . 213

Empirical Laws of Falling Bodies 213

Empirical Laws of Planetary Motion . . . 214

Gravitation applied to Moon 215

Gravitation extended to Planetary Motion 216 Gravitation extended to all Particles of

Matter 217 xvi CONTENTS

Chapter XVI Definition, Classification, And Explanation

PAGE

§ 1. Aim of Methods of Knowledge 220

§ 2. Development of Definition 221

§ 3. Nature of Definition 223

§ 4. Definition and other Modes of Stating Meaning . 226

§ 5. Limits of Definition 229

Meaning of Proper Names 230

§ 6. Rules of Definition 231

§ 7. Nature of Classification 234

§ 8. Rules of Classification . . . ^ 235

§ 9. Classification and Definition 235

Classification and Partition 237

§10. Disjunctive Classification 238

§11. Subsumptive Classification 238

§12. Provisional Character of Classification and Definition 241

§13. Classification and Explanation 242

§14. Limits of Explanation 244

§15. Logical Explanation and Familiarization .... 244

Chapter XVII Logic And Education

§ 1. General Relation of Logic to Education .... 246

§ 2. Education Relative to Society 249

§ 3. Method and Self -Activity 252

Method not Mechanical 253

§ 4. Educational Method Relative to Current Conception of Knowledge 255

Heuristic Methods 255

§ 5. Method of Science and Method of Education . . 257

§ 6. Maxims of Method 261

EXERCISES IN INFERENCE 266

INDEX 281

THE LOGICAL BASES OF EDUCATION.

Chapter I

§ 1. — Bacon begins one of the best-known of his Education essays with the words: "'What is truth?' said Knowledge. jesting Pilate j and would not stay for an answer." Whether or not this is a libel on the Roman procurator, it certainly represents a mental attitude which cannot be adopted by the educator. One of the main parts of his work is teaching. And teaching has a two-fold aspect — on the one hand it regards the pupil, and on the other it regards the subject taught. Between these two it tries to establish the relation we call knowledge. The aim of teaching is, then, to lead the pupil to attain knowledge, and to develop in him the power of using and extending that knowledge.

§ 2. — Now, if we ask ourselves what we mean by Knowledge * knowledge ' we can find no other answer than that ^^^ Truth.

IE ij it is that part of human thought which is proved true. And human thought is true just so far as it agrees with the facts of the world. All knowledge is, then, a grasp of truth. Not indeed of the whole truth : that we do not know, and never shall know. For the whole truth is the totality of reality or existence ; in other words, the universe. As this is infinite it can never be grasped by the finite human intelligence. But, as generations succeed each other, knowledge advances. Taking each new position as a fresh starting point, man uses the knowledge he has acquired as a key to unlock fresh mysteries. What was so wonderful to our forefathers that it could only be accounted for by the assumption of supernatural agency is regarded by us as commonplace. Thus the bounds of superstition are continually contracted. For superstition has play only where knowledge is absent and fancy takes its place. As Mr. Clodd remarks, " magic rules the life of the savage," ^ whilst the life of civilized man tends to become more and more completely ruled by a rational conception of law and system. Knowledge § 3 . — The thought of the modern civilized European sSpsrsti- is then, especially at first sight, very different from tion. that of the savage. But this must not blind us to

the fact that there is continuity between them ; that the former has been evolved slowly and with difficulty from the latter. " The low intellectual environment of man's barbaric past was constant in his history for thousands of years." ^ It was only when man began to think and enquire, as well as to feel and fancy, that knowledge began to take the place of belief in magic, in charms, in fairies, and in all the other apparatus by which savage man attempts to explain

^ Tom Tit Tot, p. 51. 2 Clodd, op. cit., p. 106.

the phenomena he sees about him. For modern Europe this birth of thought took place in Greece less than three thousand years ago. Since then there has been gradual advance, not however without long periods of stagnation, and even of retrogression. We need not go back very far to find superstition governing most of the life of the majority of Englishmen. King James I. believed firmly in magic, and in his book on Doemonology, he speaks of the " devil teaching how to make pictures of wax or clay, that by roasting thereof the persons that they bear the name of may be continually melted or dried away by sickness." And James was "the British Solomon." Indeed, we need not leave our own day to find many examples of the truth that whenever knowledge is absent superstition reigns. The thorough-going conception of the universality of natural law exists amongst comparatively few even in our own day. " Scratch the epiderm of the civilized man, and the barbarian is found -in the derm " says Mr. Clodd with undeniable truth. " In proof of which," he goes on, " there are more people who believe in Zadkiel's Vox Stellarum than in the Nautical A Imanac ; and rare are the households where the Book of Dreams and Fortune-Teller are not to be found in the kitchen." ^ And again : " As many a stable-door and mainmast testify, the nailing of horse shoes to ' keep off the pixies,' and, conversely, to bring luck to farmer and sailor, thrives to this day." 2 Many other examples are given by Mr. Clodd in the very interesting book from which we have quoted, and doubtless, every reader will be able to furnish additional instances. But enough has been said to illustrate the point that the outcome of ignorance is superstition.

Now, it should be noted that superstitions have ^ Op. cit., p. 97. 2 ii^i^^^ ^ 34^

B 2 their origin mainly in man's feelings and emotions, and especially in the emotion of fear, for the unknown generally inspires terror in a mmd that has little or no conception of natural law. But superstitions are not merely mental errors, they have a practical bearing, for, in so far as they are believed, they determine conduct.

Further, what has been said has made it evident that the only cure for superstition is increased knowledo-e. And this has a deep interest for the educator ; for, again to quote Mr. Clodd, " the art of life largely consists in that control of the emotions, and that diversion of them into wholesome channels, which the intellect, braced with the latest knowledge and with freedom in the apphcation of it, can alone

§ 4.— The above remarks have brought into prominence several important points which we shall do well to consider. In the first place we see that all belief is not knowledge. Belief is unquestioning acceptance by the mind. But the savage beheves as firmly in various forms of magic as the civilized man does in the law of gravitation. And his beliefs influence his actions. " The Basuto avoids the riverbank, lest, as his shadow falls on the water, a^ crocodile may seize it, and harm the owner . . . the Arabs believe that if a hyena treads on a shadow, it deprives the man of the power of speech." Now it may seem strange that such beliefs have been able to survive for so many generations the continual contradictions they must have received from experience. Indeed, this would be inexplicable were it not for another piece of experience— the fact of the marked conservatism which human nature shows with regard to its beliefs. Prejudice is an enormous ? Op. a7., p. 109. ' mU, pp. 79-80.

force in human life, and not less potent is that mental inertia which makes it hard for men to strike out a new line of thought for themselves. "It is not error," wrote Turgot, " which opposes the progress of truth ; it is indolence, obstinacy, the spirit of routine, everything that favours inaction." ^ It is only when this mental indolence is overcome, when the spirit of enquiry is roused, that men begin to ask why they believe this or that, and according to the answer to retain or reject the belief.

This leads us to see both the difference and the connexion between belief and knowledge. So far as the mental state of any individual is concerned, belief and knowledge are so far alike that both are states of full assurance of the truth of the matter in question. But they differ in this — that in the case of knowledge alone this assurance can be shown to be justified by evidence other than itself. For example a savage believes that an earthquake is the mark of the anger of some supernatural being with those who suffer its effects, but he can bring forward no evidence outside the earthquake itself to support his belief. On the other hand, the modern scientific man can show by unimpeachable evidence that the earthquake is the result of natural laws and is itself an expression of the orderly working of the universe. In thus relating the earthquake to other physical events he has replaced what was mere belief by knowledge.

There is a further and most important distinction. Belief is always an individual act. Any number of persons may, indeed, agree in believing the same thing, and this we loosely call " sharing a belief " or "holding a common faith." But the belief is not common if we use our words strictly. What is 1 Quoted by Mr. Clodd, oj). cit., p. 108.

6 THE LOGICAL iBASES OF EDUCATION chap.

common is the object of belief : each man believes for himself, each man feels his own full assurance. And this assurance he cannot communicate to another. The utmost he can do is to influence the mind of him whom he wishes to convert so as to incline him to accept the same object of belief. Belief is then, in its very essence, particular ; that is, it is the state of some one individual mind. Knowledge, on the other hand, is universal; that is, it is common to any number of minds. This is because knowledge is, as has been already said, a grasp of truth, or, as we may put it in other words, an insight into some portion of reality. It follows that knowledge is not dependent on any one individual mind, for neither the belief nor the thought of any individual can alter an element of the real world. It is true that knowledge is increased by the work of individual minds. >But once a piece of knowledge is arrived at it can be communicated to others and made common property. This is so because the evidence which establishes every piece of knowledge can be made clear. Of course, when a piece of knowledge is grasped by an individual mind, ifc is believed, and it becomes parb of the contents of that mind ; the act ci knowing is thus individual. But whilst belief is nothing beyond the act of believing, knowledge is not the mere act of knowing. For nothing is knowledge which is not based on evidence sufiicient to prove it, that is, which is not shown to be part of the order of the world. Any mind which can appreciate this evidence is forced to accept the piece of knowledge which is thus substantiated. Hence, all knowledge is in its very essence universal in its nature ; for all minds which can understand it must accept it as something not merely believed but as actually proved, and therefore known to be true.

This fact that all knowledge is of the truth, whilst belief is frequently of the false, leads us to see that the general conditions of knowledge are independent of individual beliefs. Men have, indeed, often believed they possessed knowledge when future advances have shown that their supposed knowledge was imperfect or even false. Such a mistake is easily understood when it is borne in mind that to the individual both knowledge and belief are states of full assurance ; that all knowledge is belief, though all belief is not knowledge. It is easy, then, for a man to deceive himself as to the extent to which his beliefs are really supported by sufficient evidence, and especially so since even his power to appreciate the weight of evidence is partly dependent on the amount of his knowledge. He may, then, easily confuse considerations which appeal to his prejudices and agree with his beliefs with true evidence which appeals only to his reason. Such considerations help us to see that whenever wdiat is not true has been mistaken for knowledge the reason has been that the real conditions of knowing have been departed from. When these conditions are really fulfilled, knowledge results. It will be our task in this book to examine the nature of these conditions.

§ 5 — A second point brought out by the compari- Sayage son of the thought of savages with that of civilized ^ ^ ^^'^^ ^' man is that at all times man tries to find some explanation of the world in which he lives. At every moment of his life he is brought into contact with objects and phenomena over which his wishes and feelings and thoughts have no control. The storm comes and sweeps away his hut, the sun rises and sets, the moon waxes and wanes, the clouds gather and disappear. Or again, his own actions frequently have results which he neither forsees nor desires. He eats a new berry and is ill. He steps on a stone in climbing a hill ; it gives way under him, he falls and is injured. Even consequences which he can foresee, in many cases he cannot prevent. He fails to find water and suifers thirst ; he is overtaken by the prairie fire and is burnt.

Thus even at the lowest stage of development man cannot help finding himself in the midst of a world of which he forms a part, but which exists independently of him. But the savage has not in the strict sense of the word begun to think. He is too fully occupied in keeping himself alive to concern himself with anything which has not a direct personal bearing. Especially must he be continually on guard against agencies that may work him ill. He is always finding new sources of evil to himself, and he is inclined to suspect the unknown. Savage man thus never looks at his world as a whole. Eor him it consists of isolated things and events which have a bearing — generally evil — on his own life and his own comfort. The most obvious explanation which occurs to him is to attribute to all things those powers of life which he himself possesses. Every thing is alive, or is at least the abode of a living spirit, generally of a malignant nature. Hence arises, that general belief in magic which marks all races of savages.

So, too, savage man has not learnt to distinguish between realities and symbols. Nothing is connected with a man more uniformly than his shadow ; hence it is believed that a man may be injured by doing to his shadow what would injure the man if done to himself. Similarly a man's name is believed to be an integral part of himself, and it is a universal belief amongst savages that if an enemy knows a man's name he has him in his power. Consequently, in many tribes the real names are kept secret and every individual is known by a nickname.

These few examples warn us against expecting to find any consistency in the philosophy of the savage. He attempts to explain his world not as a whole but piece by piece. He has hardly indeed begun even to ask himself what these separate objects of his experience are ; of their real properties he is profoundly ignorant. Still, he has begun to see, though most dimly, that there are relations between things. It is true that the only relations he founds his attempts at explanation upon are those of striking, but often very superficial, resemblance. Yet it is in this vague and fragmentary recognition of relations that science has its root.

§ 6. — As man begins slowly to emerge from Expianasavagery less and less of his time and energy is wSid^a?^ occupied with the mere preservation of his life. So ^^.^^^ °^ he begins to find time to feel curiosity about those things which do not immediately affect him, and even about the world as a whole. But the influence of the traditional beliefs remains strong. He still regards himself as the centre of the universe, the being for whose benefit sun, moon, stars and earth were made. Consistently Avith this he still thinks of ' things ' — i.e. material objects which can affect him through his senses — as independent pieces of reality whose nature is not affected by the relations in which they stand to each other. In other words, he regards the world as a sum of things whose relations with each other are accidental. From this point of view ' things ' are units of existence which can be re-arranged in any way, like a set of ninepins or a group of billiard balls, without altering their nature.

Within such a philosophy there is still abundant room for magic and supernatural agencies. For whilst the relations between things are regarded as indifferent and variable in any way without affecting the nature of the things related, it is obvious that those relations will not be carefully investigated, and the analogy of a living agent will still be continually called in to explain occurrences which are not understood. So fairies and witches remain part of the machinery of the world, and means must be taken to guard against their evil influence. Hence the survival of the use of charms, which is still extremely common amongst the majority of the people of Western Europe. " Many a fragment of cabalistic writing is cherished and concealed about their persons by the rustics of Western Europe as safeguards against black magic." ^

Again, so long as the relations of things are not regarded as important to the constitution of reality, and so remain unstudied, relations of striking likeness will continue to exercise undue influence over man's attempts at explanation. Thus, " doctors in the seventeenth century . . . with . . .perchance unconscious humour, gave their patients pulverized mummy to prolong their years. ' Mummie,' says Sir Thomas Browne, ' is become merchandise. Mizraim cures wounds, and Pharaoh is sold for balsams.' " ^ Even in the present day " in Suffolk and other parts of these islands, a common remedy for warts is to secretly pierce a snail or ' dodman '-Avith a gooseberrybush thorn, rub the snail on the wart, and then bury it, so that, as it decays, the wart may wither away." ^ This is quite on a level with the action of the Cheroki Indians when " to ensure a fine voice, they boil crickets and drink the liquor." ^

§ 7. — Insufficient as is the explanation of the Expianaworld which sees in it only a sum of things which woJid by ^ may enter into any relations with each other without ^^^^• affecting their own nature, it yet satisfied the mind of man till a few centuries ago. It was only with the birth of modern physical science that men really began to appreciate the importance of relations in the constitution of the world. But the old view of the independence of things still remains the philosophy of all the uneducated — that is, of all young children and of the great majority of adults. And it is from that view the educator must start in leading his pupils to a truer conception of the world. In this respect, as in so many others, the child epitomizes the evolution of the race.

It may be said, then, that modern science began with the discovery that the nature of things is affected by their relations. And this discovery was the necessary result of a deeper study of things themselves. Even to a superficial observation it was evident that many things change according to the relations in which they are placed. The clouds are scattered by the wind, the snow melts in the sun. With other things, indeed, the case seemed different, and in nothing was stability more apparent than in " the everlasting hills." But closer observation showed that even these changed continuously. Rain and frost, torrent and glacier were always at work, and their effects could be seen by the careful watcher. Thus, the idea that change is the characteristic of all things, and not a mere accident to some, began to take firmer and firmer hold of men's 1 Op. cit., p. 62. 2 j^^-^ minds, though doubtless it was long before the stage was reached which is expressed in Tennyson's lines,

" The hills are shadows and they flow From form to form and nothing stands ; They melt like mist, the solid lands, Like clouds they shape themselves and go ! " ^

Factors of But change implies an agency which causes the change. Either this agency is to be found in the nature of the thing itself, in some other thing in active relation to it, or in a combination of the two. Now, the agency of things from without is in many cases obvious. Trees and land are washed away by a torrent, smiling fields and prosperous cities are overwhelmed by a volcanic eruption, fire burns and water drowns. Hence, agency from without has seemed to some a sufficient explanation of all change. In this too we find the survival of the older belief, though under a new aspect. The older belief regarded things as essentially stable, and all change as accidental and exceptional to the general order. When change was observed it was attributed to external agency. The newer view was in opposition to this in regarding change as the normal state, but it agreed with it in attributing all change to outside agency, though the agency sought was that of material things instead of that of supernatural beings and unknown powers.

Such a view, however, cannot survive deeper critical examination. External influences are soon seen not to be the only determining factors. An acorn and a grain of corn may be planted side by side and exposed to the same influences of soil and weather, but the one will develop into an ear of corn and the other into an oak tree. It is true that

^ In Memoriam, cxxiii.

neither will develop at all apart from appropriate conditions of soil and climate, and so their development is determined by those external conditions. But it is equally clear that, given the conditions, the development which actually takes place is determined by the thing's own nature. And this nature is the essence of the thing itself. External conditions are, then, contributing factors in development, but they alone do not determine the nature of that development. A plant's life-history can be understood only when both its inner nature and its surroundings are taken into account.

In the animal world the same thing is yet more manifest. An animal is much more independent of external conditions than is a plant, for by changing his locality he may seek conditions which suit him. To the extent to which he can do this he determines his conditions rather than is determined by them. Doubtless the latter factor in his life is not absent, and in the course of ages may profoundly modify his constitution. But the mere influence of surroundings will not account for the whole of animal life.